Restore Our Future, a top super PAC backing Mitt Romney’s presidential candidacy, plans to spend $7.2 million on advertisements during the upcoming London Olympics, according to reports.

The major ad push will more than counter the $6.5 million of Olympic air time purchased by President Obama’s reelection campaign. And it is an opportunity to link Romney to one of his most universally heralded achievements—his management of the Salt Lake City Olympics 10 years ago.

Restore Our Future’s ad buy was reported Thursday morning by Politico and CNN. The content of the ads is unknown, but they will run between July 31 and Aug. 9 in 11 swing states: Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, North Carolina, Ohio, Pennsylvania, Virginia, and Wisconsin.

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The ad campaign is the latest signal that Restore Our Future is ramping up its general election efforts. Only two weeks ago, the group announced a $7.6 million buy in nine swing states.

Even before the recent splurges, Restore Our Future had spent $53.9 million through the end of May, according to campaign finance data maintained by the nonpartisan Center for Responsive Politics. The group’s $61.5 million raised was more than quadruple the total collected by Priorities USA Action, the leading super PAC supporting Obama.

The Globe reported Thursday that on the whole, super PACs supporting Republicans have outraised those backing Democrats by a 3-1 margin: $158 million to $47 million.

Super PACs are independent groups that can accept uncapped donations from individuals, corporations and labor unions but cannot coordinate spending with candidates’ official campaigns.

Callum Borchers can be reached at callum.borchers@globe.com. Follow him on Twitter @callumborchers.